Descents of unipotent cuspidal representations of finite classical groups

On the Gan-Gross-Prasad problem for finite classical groups

“…We obtain the following immediate consequence by Theorem 1.4, Proposition 3.2 and Theorem 1.1 in [LW3].…”

“…[GGP1,Theorem 16.1]) (c.f. [LW3] for details in this case). According to whether π and σ are complex irreducible representations of orthogonal groups or symplectic groups, the above Hom space is called the Bessel model or Fourier-Jacobi model.…”

“…However, we can not get the the multiplicity one in the Gan-Gross-Prasad problem for arbitrary representations directly in this way. In previous works [LW2,LW3,LW4], we have studied the Gan-Gross-Prasad problem of unipotent representations of finite unitary groups and the descent problem of unipotent cuspidal representations of finite orthogonal groups and finite symplectic groups. In this paper, we generalize our previous results and our main tool is the theta correspondence over finite fields.…”

Lusztig correspondence and the Gan-Gross-Prasad problem

“…However, we can not get the complete answer in the Gan-Gross-Prasad problem directly in this way. In previous works [LW1,LW3], we have studied the Gan-Gross-Prasad problem of unipotent representations of finite unitary groups and in [LW2,Wang] for finite orthogonal groups and finite symplectic groups. In this paper, we will give a formula to reduce the Gan-Gross-Prasad problem of arbitrary representations to the unipotent representations, which is known in our previous work.…”

“…[GGP1,Theorem 16.1]) (c.f. [LW1,LW2] for details). If π and σ are complex irreducible representations of orthogonal groups, then the above Hom space is called the Bessel model.…”